INTRODUCTION TO DLVO THEORY

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INTRODUCTION TO DLVO THEORY
By Sanjay Kumar MohantyDept. of Civil
Environmental Engineering University of Hawaii at
Manoa
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DLVO THEORY

• Goal
• Develop an understanding of the fundamentals of
  particle adhesion
• Objectives
• Quantify interaction forces between particles
  and surfaces in varying solution chemistries
• Examine force trends as a function of solution
  pH and ionic strength

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Basic concepts of DLVO theory
Charged colloidal particles suspended in water
should interact through Van-der-Waals attractions
and Coulomb interactions. Added salt causes a
screening of the Coulomb repulsion (DLVO-theory),
added small particles (or polymer chains) may
lead to attractive forces by the so-called
depletion mechanism
Existence of an attractive pair potential between
like-charged particles.
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Origin of surface charge
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• For particles attached to the surface
• EDL forces are weak
• van der Waals forces are relatively significant
• To describe particle adhesion in close contact
• van der Waals forces, chemical bonding are
  dominant

Double Layer Repulsion
Total
van der Waals attraction
Bulk solution
Diffuse Layer
Stern Layer
Negatively charged surface
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Ionic solids
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Metal oxide

• PDIproton hydroxyl ion

Surface (dissolved) proton concentration   HS
H exp-Fy/RT here surface charge
conc. depends on pH

• PZC can be determined using pKa values

• Surface hydroxyl dissociation
• gtMOH2 or ?MOH2
• gtMOH or ?MOH
• gtMO- or ?MO-

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Log C-pH diagram

• Surface chemistry on log C-pH

pKa1
pKa2
?M-O-
?M-OH2
?M-OH
pHpzc
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• Depicting surface charge on log C-pH

pHpzc
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Electrostatic Models

• Electrostatic models
• Constant capacitance
• adsorbing ions on single layer
• linear decrease in surface potential
• Diffuse double layer (Gouy-Chapman)
• adsorbing ions on single layer
• diffuse double layer
• exponential decrease in surface potential
• Triple-layer (Stern)
• two layers of adsorbing ions
• diffuse double layer, exponential decrease

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Gouy-Chapman double layer model

• Classical Electrical Double Layer Theory
• Surface Density (?p)
• ?s ?o ?p
• Gouy-Chapman Theory
• Electroneutrality
• ?p ?d ?s ?o ?d 0
• Poisson - Boltzmann Equation
• ?d -0.1174 ?I sinh (ze?o) / (2 ? T)
• Electric Potential
• ?o ?d

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• Diffuse Double Layer
• charge potentialz is valence of ion in
  double layer
• adjustable parameters
• K, K-
• applicable at low I (lt0.1 M)

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THE GOUY-CHAPMAN MODEL (a) 





CHARGE DISTRIBUTION
POTENTIAL
DISTRIBUTION
The electric double layer ? Consists of a surf.
layer of charge on the solid surface, i.e.,
surface charge (so). ? The surface charge is
balanced by a diffuse layer of counter-ion charge
(sd) located at the aqueous side of the
interface visualized as point charges.
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Na
Na
Na
Cl-
Na
Cl-
Na
Cl-
Na
Cl-
Na
Na
Na
Cl-
?p
?d
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The Stern Model
? Accounts for ionic size by locating the centers
of the first layer of ions at a mean distance d
from the solid surface.   ? Beyond the first
layer, the ionic distribution follows the
Gouy-Chapman picture of a diffuse layer based on
point charges
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Stern model
If neglect of the second capacitance (i.e., C2)
has no significant effect on the predicted
properties of the electrified interface, then Y1
and Y2 may be equated.   The total interfacial
capacitance then becomes 1/CT 1/C1
1/Cd
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  When potentials and ionic strengths are
relatively low, the capacitance associated with
the compact layer (i.e., C1) far exceeds the
diffuse layer capacitance.   ? Stern model
reduces to the diffuse layer model (Gouy-Chapman
model) ? total interfacial capacitance is
provided by the diffuse layer, i.e., 1/CT
1/Cd
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CONSTANT CAPACITANCE MODEL   When potentials and
ionic strengths are high, the diffuse layer
capacitance is relatively greater than the
compact layer capacitance.   ? Stern model
reduces to the constant capacitance model, where
the total interfacial capacitance is given by
1/C 1/C1
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Surface Complexation Theory

• Classical Electrical Double Layer Theory
• Stern-Grahame Theory
• Electroneutrality (if ?s 0)
• ?o ?? ?d 0
• Poisson - Boltzmann Equation
• ?d -0.1174 ?I sinh (ze?d) / (2 ? T)
• Electric Potential
• ?o - ?? ?o / C1
• ?? - ?d (?o ?? ) / C2 - ?d / C2

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THE GOUY-CHAPMAN-STERN-GRAHAME (GCSG) ELECTRIC
DOUBLE LAYER     ? Ascribe sizes to the ions
right next to the Stern plane.   ? Ions in the
Stern plane considered to have lost their waters
of hydration.   ? Ions in diffuse layer retain
hydration shells.  
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THE GCSG ELECTRIC DOUBLE LAYER                   
  Stern layer can be subdivided into (a) First
layer of dehydrated ions (Inner Helmholtz Plane
(IHP)) potential, yb charge, sb. (b) First
layer of hydrated ions (Outer Helmholtz Plane
(OHP)) the OHP marks beginning of the diffuse
layer. Eneutrality condn so
sb sd 0
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• Schematic Description of Models

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Conclusions

• Importance and Applications
• Surface Complexation Theory
• Constant Capacitance
• Double Layer
• Triple Layer
• Model Performance

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Thank You ?, Any Questions?
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• Describes both electrostatic double layer (EDL)
  and van der Waals forces
• Van der Waals forces
• Attractive forces which dominate at small
  separation distances
• Generally not a function of solution pH or ionic
  strength

Ftotal Fvan der Waals FEDL

• Electric double layer forces
• Repulsive forces which dominate at larger
  separation distances
• Stern layer tightly bound ions
• Diffuse layer free ions that rapidly exchange
  with ions in the Stern layer
• Zeta potential at break between Stern and diffuse
  layers
• EDL thickness is a function of pH and ionic
  strength of solution

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Definitions..
 The point of zero charge (pzc) Bulk aqueous
phase concentration (or more precisely, activity)
of potential-determining ions which gives zero
surface charge
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Determining Force Trends

• Vary 3 parameters surface, pH, ionic strength
• Generate force curves using atomic force
  microscope (AFM)
• Calculate pull-off forces
• Plot pull-off forces as a function of roughness,
  pH and ionic strength

Pull-off force
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Metal oxide

• Permanent charge on faces
• isomorphic substitution of silica tetrahedra
• Al3 for Si4 ? negative charge
• Amphoteric charge on edges
• ?Al-OH2 H ?Al-OH
• ?Al-OH H ?Al-O-
• edge pHpzc 7-8
• Net surface charge
• pHpzc 2-5

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Carbonates

• protonation of carbonate functional groups
• MCO3H2
• MCO3H
• MCO32-
• point of zero charge depends on
• PCO2 controls carbonate solution species
• M concentration (e.g., Ca2)
• at normal PCO2, pHpzc 7-8

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Applications

• Surface Complexation Theory
• Importance
• Applications
• Industrial discharge or acid mine drainage in
  rivers
• Lakes and oceans
• Transport of solutes in soils and aquifers
• Drinking water and wastewater treatment

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Triple layer model
  The solid/liquid interface visualized in terms
of three layers of charge
First layer innermost layer, the surface layer
consists of the solid surface itself locale of
primary potential determining ions (e.g., H, OH-
for a metal oxide).   The charge and potential
associated with this layer are designated as so
and Yo respectively.
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The solid/liquid interface visualized in terms of
three layers of of charge
 Second layer the inner Helmholtz plane (IHP), a
compact layer of counter-charge typically
consisting of relatively strongly bound (i.e.
specifically adsorbed) ions.   The
corresponding charge and potential are identified
as s1 and Y1 respectively.
Third layer the diffuse layer, the location of
ions, termed indifferent ions, ions only weakly
attracted to the solid surface.   The plane of
the diffuse layer closest to the solid surface is
designated the outer Helmholtz plane (OHP).
The potential at the OHP is Y2 and the charge
associated with the diffuse layer is s2.  
Three capacitances in series C1, representing
the region bounded by the surface plane and the
IHP  C2, representing the region bounded by the
IHP and the OHP Cd, representing the diffuse
layer capacitance
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• Triple Layer Model
• Stern model for adsorbed ion planes
• adjustable parameters
• K, K-
• C1, C2

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Three capacitances in series  Thus, total
interfacial capacitance CT  1/CT 1/C1
1/C2 1/Cd  Relationship between charge
and potential in the first two layers   so
C1(Yo -Y1) s1 C2(Y1 -Y2)
TRIPLE LAYER MODEL ELECTROSTATIC
CONSIDERNS  Relationship between the diffuse
layer charge (s2), the potential (Y2) at the OHP,
and the concentration (Cb) of the electrolyte in
the bulk solution  s2 -(8eRTCb)1/2 sinh
(FY2/2RT) -0.1174 Cb1/2 sinh (FY2/2RT), at
25C The diffuse layer capacitance is then
given by   Cd ds2/dY2  The electrified
interface must satisfy the electroneutrality
condition. Thus  so s1 s2 0
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TRIPLE LAYER MODEL ELECTROSTATIC
CONSIDERNS Three capacitances in
series   Thus, total interfacial capacitance
CT   1/CT 1/C1 1/C2
1/Cd   Relationship between charge and potential
in the first two layers   so C1(Yo
-Y1) s1 C2(Y1 -Y2)
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TRIPLE LAYER MODEL ELECTROSTATIC
CONSIDERNS   Relationship between the diffuse
layer charge (s2), the potential (Y2) at the OHP,
and the concentration (Cb) of the electrolyte in
the bulk solution   s2 -(8eRTCb)1/2 sinh
(FY2/2RT) -0.1174 Cb1/2 sinh (FY2/2RT), at
25C The diffuse layer capacitance is then
given by   Cd ds2/dY2   The
electrified interface must satisfy the
electroneutrality condition. Thus   so s1
s2 0  
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Surface Complexation Theory

• Classical Electrical Double Layer Theory
• EDL at Oxide Surfaces
• Nernst equation
• ?o F ( ? - ?- )
• ?o 2.3 RT F-1 (pCpzc- pC)
• Proton Surface Charge
• ?H ( ?H - ?OH- )
• pHpzc
• Zeta Potential
• Isoelectric Point